Cycle LDPC code

Cycle LDPC code[1]

Also known as Non-binary LDPC (NBDPC) code.

A \(q\)-ary LDPC code whose parity-check matrix has weight-two columns. Non-binary cycle LDPC codes for \(q\geq 32\) exihibit good performance [2–4].

The minimum distance of a binary cycle LDPC code is \(d\geq g/2\), where \(g\) is the girth of the code's Tanner graph [5].

Binary cycle LDPC codes are not asymptotically good [6].

Linear-time encoder [7].

Cycle LDPC codes have been proposed to be used for MIMO channels [8].

[1]: S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI
[2]: X.-Yu. Hu and E. Eleftheriou, “Binary representation of cycle Tanner-graph GF(2/sup b/) codes”, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577) (2004) DOI
[3]: R.-H. Peng and R.-R. Chen, “Design of Nonbinary Quasi-Cyclic LDPC Cycle Codes”, 2007 IEEE Information Theory Workshop (2007) DOI
[4]: C. Poulliat, M. Fossorier, and D. Declercq, “Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images”, IEEE Transactions on Communications 56, 1626 (2008) DOI
[5]: C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[6]: L. Decreusefond and G. Zemor, “On the error-correcting capabilities of cycle codes of graphs”, Proceedings of 1994 IEEE International Symposium on Information Theory DOI
[7]: Jie Huang and Jinkang Zhu, “Linear time encoding of cycle GF(2/sup P)/ codes through graph analysis”, IEEE Communications Letters 10, 369 (2006) DOI
[8]: Ronghui Peng and Rong-Rong Chen, “Application of Nonbinary LDPC Cycle Codes to MIMO Channels”, IEEE Transactions on Wireless Communications 7, 2020 (2008) DOI

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“Cycle LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/cycle_ldpc